$$ \begin{aligned} \frac{\frac{1}{6}}{x} &= \frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ x\cdot6\cdot4 }. \\[1 em]x\cdot6\cdot4 \cdot \frac{\frac{1}{6}}{x} &= x\cdot6\cdot4\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]4 &= 6x&& \text{ swap the left and right side of the equation } \\[1 em]6x &= 4&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{4}{6}&& \\[1 em]x &= \frac{2}{3}&& \\[1 em] \end{aligned} $$

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